From Spin Glasses to Negative-Weight Percolation

verfasst von: Alexander K. Hartmann, Oliver Melchert, Christoph Norrenbrock
Abstract: Spin glasses are prototypical random systems modelling magnetic alloys. One important way to investigate spin glass models is to study domain walls. For two dimensions, this can be algorithmically understood as the calculation of a shortest path, which allows for negative distances or weights. This led to the creation of the negative weight percolation (NWP) model, which is presented here along with all necessary basics from spin glasses, graph theory and corresponding algorithms. The algorithmic approach involves a mapping to the classical matching problem for graphs. In addition, a summary of results is given, which were obtained during the past decade. This includes the study of percolation transitions in dimension from d = 2 up to and beyond the upper critical dimension d_u = 6, also for random graphs. It is shown that NWP is in a different universality class than standard percolation. Furthermore, the question of whether NWP exhibits properties of Stochastic-Loewner Evolution is addressed and recent results for directed NWP are presented.
Organisationseinheit(en): PhoenixD: Simulation, Fabrikation und Anwendung optischer Systeme
Institut für Quantenoptik
Externe Organisation(en): Carl von Ossietzky Universität Oldenburg
Typ: Übersichtsarbeit
Journal: Entropy
Band: 21
ISSN: 1099-4300
Publikationsdatum: 02.2019
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Information systems, Mathematische Physik, Physik und Astronomie (sonstige), Elektrotechnik und Elektronik
Elektronische Version(en): https://doi.org/10.3390/e21020193 (Zugang: Offen)
https://doi.org/10.15488/10963 (Zugang: Offen)